Analysis of Unitarity in Conformal Quantum Gravity

Abstract

We perform a canonical quantization of Weyl's conformal gravity by means of the covariant operator formalism and investigate the unitarity of the resulting quantum theory. After reducing the originally fourth order theory to second order in time derivatives via the introduction of an auxiliary tensor field, we identify the full Fock space of quantum states under a BRST construction that includes Faddeev-Popov ghost fields corresponding to Weyl transformations. Using the Kugo-Ojima quartet mechanism, we identify the physical subspace of quantum states and find that the subspace containing the transverse spin-2 states comes equipped with an indefinite inner product metric and a one-particle Hamiltonian that possesses only a single eigenstate. We construct the LSZ reduction formula for the S-matrix in this spin-2 subspace and find that unitarity is violated in scattering events. The explicit way in which this violation occurs represents a new view on the ghost-problem in quadratic theories of quantum gravity.

arXiv commentv2: 31+11 pages, discussion changed and references added

References in corpus (17)

• Local BRST cohomology in gauge theories
• Degenerate higher derivative theories beyond Horndeski: evading the Ostrogradski instability
• No-ghost theorem for the fourth-order derivative Pais-Uhlenbeck oscillator model
• xTras: a field-theory inspired xAct package for Mathematica
• xPerm: fast index canonicalization for tensor computer algebra
• xPert: Computer algebra for metric perturbation theory
• Aspects of Quadratic Gravity
• Unitarity, stability and loops of unstable ghosts
• Fakeons And Lee-Wick Models
• Agravity up to infinite energy
• Quantum mechanics of 4-derivative theories
• The Ostrogradsky instability can be overcome by quantum physics
• BRST Symmetry and Cohomology
• Covariant BRST Quantization of Unimodular Gravity I -- Formulation with antisymmetric tensor ghosts --
• Conformal Anomaly for Non-Conformal Scalar Fields
• On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model
• FieldsX -- An extension package for the xAct tensor computer algebra suite to include fermions, gauge fields and BRST cohomology

Cited by in corpus (4)

• Spontaneous Conformal Symmetry Breaking and Quantum Quadratic Gravity
• Unitarity through PT symmetry in Quantum Quadratic Gravity
• High-energy properties of the graviton scattering in quadratic gravity
• Primordial Gravitational Waves in Quadratic Gravity